Find the following values for a lump sum:

a$.$ The future value of $$500$ invested at $8\%$ for one year

b$.$ The future value of $$500$ invested at $8\%$ for five years

c$.$ The present value of $$500$ to be received in one year when the opportunity cost rate is $8\%$

d$.$ The present value of $$500$ to be received in five years when the opportunity cost rate is $8\%$ assuming:

Annual compounding

Semiannual compounding

Quarterly compounding

$2)$ What is the effective annual rate $($EAR$)$ if the stated rate is $8$ percent and compounding occurs semiannually? Quarterly?

$3)$ Find the following values assuming a regular, or ordinary, annuity:

$4)$ Consider the following uneven cash flow stream:

Year Cash Flow

$0$ $$0$

$1$ $$250$

$2$ $$400$

$3$ $$500$

$4$ $$600$

$5$ $$600$

a$.$ What is the present $($Year $0)$ value if the opportunity cost $($discount$)$ rate is $10$ percent?

b$.$ Add an outflow $($or cost$)$ of $$1,000$ at Year $0.$ What is the present value $($or net present value$)$ of the stream?

$5)$ What is the present value of a perpetuity of $$100$ per year if the appropriate discount rate is $7\%?$ Suppose that interest rates doubled in the economy and the appropriate discount rate is now $14\%.$ What would happen to the present value of the perpetuity?

$6)$ Consider the following investment cash flows:

Year Cash Flow

$0-$$$1,000$

$1$ $$250$

$2$ $$400$

$3$ $$500$

$4$ $$600$

$5$ $$600$

a$.$ What is the return expected on this investment measured in dollar terms if the opportunity cost rate is $10\%?$

b$.$ Provide an explanation, in economic terms, of your answer.

c$.$ What is the return on this investment measured in percentage terms?

d$.$ Should this investment be made? Explain your answer.

$7)$ Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine:

a$.$ What is the expected rate of return on the project?

b$.$ What is the project's standard deviation of returns?

c$.$ What is the project's coefficient of variation $($CV$)$ of returns?

d$.$ What type of risk does the standard deviation and CV measure?

e$.$ In what situation is this risk relevant?

$8)$ Suppose you won the lottery and was offered a choice of two prizes:

$$500,000$ in cash or

A coin$-$toss gamble in which you would win $$1$ million if a head were flipped and nothing if a tail were flipped.

a$.$ What is the expected dollar return on the gamble?

b$.$ Should you choose the sure $$500,000$ or the gamble?

c$.$ If you chose the $$500,000$ gamble, are you a risk averter or a risk seeker?

$9)$ Suppose that Apex Health Services has four different projects. These projects are listed below, along with the amount of capital invested and estimated corporate and market betas:

a$.$ What is the overall market beta of Apex Health Services?

b$.$ How does the riskiness of Apex's stock compare with the riskiness of an average stock?

c$.$ Would stock investors require a rate of return on Apex that is greater than, less than, or the same as the return on an average$-$risk stock?

$10)$ The market, in general, and two healthcare stocks have had the following returns over the past four years:

a$.$ The risk$-$free rate is $7$ percent. The market risk premium is $5$ percent. The expected rate of return on both stocks is $12$ percent. Which stock would you purchase?